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Extra resources for Funktionentheorie 1: Grundlagen
Proof: Define , the set admits at least one solution is connected. e in [a, by putting, for every and y is not a local extremum point for f(t, x, z, Â·)}. 1 of  holds and, by standard arguments, it is easy to prove that the multifunction Q has non-empty closed values and is lower semicontinuous (see [2,17]). Using Vitaliâ s covering theorem and Lusinâ s theorem, yields a sequence non-empty, closed subsets of [a, b] such that we set of pairwise disjoint, , and is continuous. Now, Â Owing to Lemma 5 in , the multifunction is lower semi-continuous as a simple computation shows.
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